Integrated Calendar

To bridge the microscopic molecular motion in complex structures with the macroscopic diffusion given by the Magnetic Resonance (MR) signal, we propose a general stochastic model for molecular motion in a magnetic field. In this model, the Fokker-Planck equation governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad hoc selection of a propagator. The boundary conditions that implicitly describe the microstructure of the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal.
In the second part of the talk, we will utilize our knowledge about the Bloch Torrey equation to quantify the effect of self-diffusion on multi-parametric sequences, such as those used for Magnetic Resonance Fingerprinting (MRF). We propose a signal simulation approach, generate dictionaries based parameter estimation that replaces the Bloch equation with the Bloch-Torrey equation, and accounts for protocol and scan dependent parameters. We apply this framework to a Multi Spin Echo (MSE) protocol and quantify the diffusion encoding introduced by the spoiler gradients in this sequence. We further show that increasing the spoiler strength would allow detecting the diffusion by including the diffusion effect in the dictionary.